The expectancy of solving an item successfully and the personal value of taking the test are considered antecedents of test-taking engagement.
However, the perceived expectancy of being capable of solving an item may vary considerably across test-takers (Asseburg and Frey 2013; Cole et al. 2008).
The probability of solving an item depends only on the respondent's ability, or proficiency, and two item parameters characterizing the properties of the item (item difficulty and item discrimination).
These two parameters relate negatively (θi – δi), because the probability of solving an item increases with the person's ability but decreases with greater item difficulty (Wright & Stone, 1979).
Traditional approaches to measurement scales rely on averages or a simple summation of the test scores; IRT models instead reflect the assumption that the probability of solving an item depends on the test taker's latent trait or ability (i.e., θi = person parameter), combined with the item difficulty (i.e., δi = item parameter).
In this paper, we suggest a parallel algorithm based on a shared memory SIMD architecture for solving an n item subset-sum problem in time O(2n/2/p) by using p = 2q processors, 0⩽q⩽n2−2log2n.
For example, to solve item 20 (item difficulty = −.274 logits) (outlined in section "Research questions") correctly, two mental processes are relevant: (a) matching as scientific authors' statements have to be compared with statistical values; and (b) specifying as the test persons have to "identify principles that apply to a specific situation" (Marzano and Kendall 2007, p. 50).
A typical application of model (1) is psychometrics, with θ v describing respondent's v ability to solve a task (or item) and β i describing the difficulty of task (or item) i.
Hariri et al. (1995) used GP technique to solve an inventory model with multiple items that having price discount.
For instance, students had to solve a number of math items by applying arithmetic and combinatorial operations (OECD [2005]).
